Gently wash mushrooms and remove gills. Place the mushroom caps with the gill side up, on a rimmed baking sheet; drizzle with oil and vinegar, and season with salt and pepper.
Bake until caps are just tender, about 15 minutes. Top with leeks, spinach, and cheese; season again with salt and pepper. Bake until spinach wilts and cheese starts to brown, about 10 to 12 minutes.